Sometimes people say that water is removed from clothes in a spin dryer by cent*u6w4vxr5 0(lmbnw v prifugal force throwinnvb*u 0wx 6mvp4l(w 5rg the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp ch6 +cchz.h/h eurve at a constant 60 kh .+h6he/zc chm/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the caa)wnkt cp6h/i-sv +x h6xy+4ur exert the greatest and least forces on th-4va yxtw+n6kx+ ph c6/i su)he road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a 0vt-7 o0,oefywa yv h2horse on a merry-go-round. Wh0o -e y7vo,ha2 wf0tvyich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water sp .(, xy6v-pnnokzxt.y illing out, even at the top of the circle when the bucket is up-.k, xpo6(zv yyntn. xside down. Explain.

How many “accelerators” do you have ibiu 7r2c fb4r ln5 ci (2fiub8f9(9-svwuo8eon your car? There are at least three controls in the car which can be used to cause the car to accelera-o88(nle2f59u fwio 9(ucc2vi r r7bbf4sibute. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fifr.n0pgx xw)hf,4d eogk*.5 gg. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feel xef,4d*w5.pg0o.fx kgg )nrh s the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve a,blfde,9t.v lyk * h2ot high speed?

Why do airplanes bank when they turn? Howf *q++t5cjsp b y5sol. would you compute the banking angle given its speed andb*s 5 o+l5y.c+sjptfq radius of the turn?

A girl is whirling a ball on a string ar ny. y xy*vo3a , 6ebf,n+pusswk32e.xound her head in a horizontal plane. She wants to let go at precisely th*b, w6+eno.yn3y spyxu2akfvex ,s3. e right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hocb v*d8g:un+rz3q s8mw large a force? Consider an a rn:gz*q8c v3 b+mud8spple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbi:xac ezmhv ,6/5f8psipg.dj(t bp/jhdez 5: fp ig(,axc6m8.vse different?

Which pulls harder gravitationally, the Earth on the 5) pmoqlj0q*zusq2 5 zutow n75ho7c;Moon, or the Moon on the Earth? Which acceleratu tcoh72pqq 5m7juzn5zs) o;5q lw0o *es more?

The Sun's gravitational pull on the Earth is much larger than the Moon'm- b76szwpljx8upm 6* s. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference bsm-pxm8* 7lj upw66 zin gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at thin*pkd *krd xh1s91r)e poles? What two effects are at work? Do they oppose each ox* r1pddr*h) sknk19 ither?

The gravitational force on the Moon due to the Earth is only about half th pcu364/ zae yt-zdk4xu +zz0qe force on the Moon due to 03 uk4-zzz6de/ zux +cyq4pta the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in i t9z : xbtc0x)v0m8gcat)2jvtts orbit around the Sun larger or smaller than the centripetal acceleration of thx09vxmgttzj t)c )a2t c8 :vb0e Earth?

Would it require less speed to launch a satell+4hg ijud7r *hiz(s 9fj /;gqlite (a) toward the east or (b) toward the w g+ z(4i jqdlrhgsjf ih/9u;7*est? Consider the Earth’s rotation direction.

When will your apparent weight b7smv *:2i4oqg xabg v)e the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerat)4oavg*i 7:m sb2gvqxes upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected by 85ky h r6;bqcs4o3mi,zi , gnpweightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig.3b i5 o8s,p q4igz,hcymrk ;n6 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner exkdwd59.on;-e2pajwkf i: cz*( 5wmg xperiences “free fall” or “apparent weightlessness” between stepgx5ji5k *; azdkd w:9ecw2p.m-n( wfo s.

The Earth moves faster inf znmil0e4wrkem / fil9q0 b 59ci(i*dc-. 6hn its orbit around the Sun in January than in July. Is the Earth closer to the Sun in0n*5b(c6 eqnm z99iw -rliifieh4f0c lk.d/ m January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until i w)m6m4 g0*rmtm caa:zt was discovered to have a moon. Explain how this discovery enabledc :am mg0*t4 r)zm6wma an estimate of Pluto’s mass.

  The Sun's gravitational pull on ah.c*j lx.5fj/elkqcs n j41 /the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides.l.hlcfq c k*/jex5jj/n s14a. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling z*lvh5n3 j i;d 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleratlxt wnt6o/19 3kbb67 ruz,kec))u upmion of the Earth in its orbit around the Sun, and the net force exerted on the tl7m1 z6 rtc6x/9bu ,b)uop3kwku e)n Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 ).b d5hjmk+ p x3ojof,N is exerted on a 2.0-kg discus as it rotates uniformly k dh,bj+o)fpj 3x.o5m in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shutt:42+lr d 0a.bcnty4qd )kzlydt mp;:qle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the c k)0 lqny:4ydm 4 :;2tdtl ca.bdpqzr+entripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude ouuqz.2qk2gtg orr/ 64 f the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (r4u. 2qzu6gt2 oqkgr/revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verticah4sbh2 l2rh ops,dv p6/.ctd6/p.arbl circle of radius 72.0 cm , as ssdr2b.v, r2h4 s6oh./h 6tppplb d/achown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a t /b* 3r**ozqs+wi-e*tc 80fbdg mksji urn of radius 77 m on a flat road if the coefficient of static friction between tires swm r * j+cb*k3f sz-idobt8/i*e0q *gand road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be bldzyo ;:gxiry 9( j- 5nom;,pxetween the tires and the road if a car is to round a level curve of radius 85 m at a speed or;:il;d9ymoj 5,z o -yxx(gpnf 95km/h ?   

  A device for training astronauts and jyw6 nss2abm)1 et fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the train2 s 1)mb6saywnee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axhfkpw6gdir srz 31uoln)*2*zw m5m4 2is of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the *4i 3 )2z*f gh wwrmrmd5z26su1kolnp coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coass (jpa662dox czi m 7q/(rvip2ter be traveling when upside down at the top q(z p2x 6dosijm vc/6ap(ir27of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including theqqy y2 tv9fg4j5b*wan71(njc cpo 5s) driver) crosses the rounded top of a hiq7o (ay) bt41q5ncvj*n5scyp fgwj9 2ll (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheeluifs7qy pj.g67 4h 0 yflbxwy*rv+3,-i8ptnc need to make for the passengers to feel “weightless +07tq-4c gyyvyblhx wf6r*3 .j8i nisp ,p7fu” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiusgtt0g:+7rv:zdt6oqm 6m3o (xd )pi yg 1.10 m. At the lowest point of itsd: qzgt )t63 mxygdo(: 6r om0v7pt+gi motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the a ;bd6hme1-7 pbnbd1 uuc0o+uyqb75m t xis of rotation isbdeb71nyuq uc1 d b6p+bt;oh -0 m5um7 to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people a7y;rbk vtp*g 5aj:1xmopq na(tg.h2 ;re rotated in a cylindrically walled "room." (See Fim. q y:gb7 2ptoat;hrpnka vjx5;*( g1g. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey td( nd c( jeoy;x;gj 2tmn559jsable(jec 2tjnsd9yd;5jxg5(m no ;top, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of u, bfv3z3eez7 7h;y ywqt;e5qthe ball which revolves on a string 0.600 m long. In partictqyev,;b eh53;7ew3qz7uz y fular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked w - tw 2itd.c,aou0/bxy3)ann for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesx:c0w 8:equ diu55kdg7za1ao $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an r9.:o2v y va myb 2s8og-sxc*oevasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangentijk3ge2 3 ,n.sug8im vaal and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its evknu,ji38g.m3a 2gs speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pi1f1pofh 8 hph/t area, going from rest to 320km/h in a semicircular arc with 1hphh o18ff/pa radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circlewla2a4vo4bn s4p 6 n/7fxwex) of radius 2.90 m . At a particular instant, its acc 2wlxn sp v4e 47aaf/4)nb6xwoeleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earthb+jx 56teet 6e’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass t5 6x6ebje e+tis 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mar0 rean y +2+n)ttsyh:gnitude of 12 m/sryh tne +a)r0n2ts+:y$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's ra eyj6g 9u,/srldius is 1.74 yr/sugj,6l9 e$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times b. uze28snt tx asc:hdc0+ ,;xthat of Earth, but has the same mass. What is the acceleratics xt,hc ;zs:0+n8a2. xebtduon due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiuxyzyh)rt 9tz 7giz 5)6s. What is g near ity7yt6z5)xzzg )hi9 trs surface?   

  Two objects attract each other gravitationally with a force ofoa r( aqdc)l(4 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravi cxol;)r7. oldk+y/k5al k,1wadp(ypty, at (a) 3200 m ,ara;x.1loy cdkd oy)p 5 w/kl7k(lp+    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whex-w,k, ari 2ijag/ei0fs0my4jes 4a: re thegravitational accelera 24j/y0fagm ajri s0-w eix,,sa4ei: ktion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five time-rho:bw;e2m-f (qtz iyg38u ls the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on gy8m(:3-ob ; qlze-2trfw hiuthis monster.    $\times10^12$

  A typical white-dwarf star, which once was an average stasm)8lpiit) m0 qd-bi1 r like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surfac10ipm-dsb )q i 8lti)me gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in theaoj4msm 32+6-fjo s vo space shuttle. Your friends respond that they thought gravity was just a lot weaker ums4vjo aosjm+63 -2fo p there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners o .3i4l)usw rvff a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational fwv3l ) .4ufirsorce exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yearsyh09 dtr qu 88zj+ogd: most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (yg+doj8u d9t q h8:r0zFig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleratiow4)bc1f3qtwn:1 bprb n of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determineqbw 4) rf1c3b:wpnb1t the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun 0./ew7mntkkq,f lm(x using the known value for the period of the Earth and its distance from the Sun. [Nomf teklm(x/q wk07, .nte: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in plc4/ e9yu*w oa stable circular orbit about the Earth at a height of 3600ycp*lu/w 4 o9e km.    $\times 10^3$

  The space shuttle releases a satelzj1 -g:my-yx et8 q dmmz+0r5tu3qp9z lite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurty0p qz9+mm3-1 jrzg:ez-u 85xmdy tqs?    $\times 10^3$

  At what rate must a cyliynchlpjue4 8*9 1ixm )ndrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and u*9 i4p)l8yhem1cjxngive your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eare evnoq ol.d2rf8e)4g,t g4gb 3qq l/3th in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to gqg rqndlov,) 23 l.fqob8e4g3/ e4 tethe radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched f) qt y n shf;m0hp(,jum.:gt/urom the top of Mt.m j)uugth0p;tm qh:,n/(f s.y Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module conttj +uum,co,r;v8s,xm;+ hx)vlzs(bt 3xf* xfinued to orbit the Moon at an altitude of about 100 km. How long did it take to go around thexl,*(xsvf; 8,ht urcsxzbm,+mft )u;3 j +ovx Moon once?    s

  The rings of Saturn are composed of chunks of ip* +a owc5s/t5s 5h+v5dfyxuqce that orbit the planet. The inner radius of the rings + t5ss 5q xu5wp*/y+ofhavc5d is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Wheqlv-rd* 20h f55qzdiat is the ratio of a person’s apparenqq dr 025f-* lzvi5dhet weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of q 5ug75a 8fss8s)rcbt a 75-kg astronaut 4200 km from the center of the Earth's Moon )7ssfs5a8qg 5curt8b in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star s(rb(xb)nsilg h5/ p 7tystem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. xi7 5r(b(lhngbt) s/pWhat is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight78a*i41 c9jbvu wst at of a 55-kg woman in an elevator that movesi 9aa4w t1csb*tvj u87
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from 0xe52uw 4ui 1mxt*lgia cord suspended from the ceiling of an elevator. The cord can withstandg i u4ilm*tue12x5 x0w a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a +*wyv7lwl43v 9qekzd planet with period T , the density (mass/volumwvzl3d49qvw7 *yk el+e) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the perif8v1n s5ed wq;od of an artificial satellite o s5v1ewqf;nd 8rbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mez 8lx ijqc;;:rters across, orbits the Sun like the planets. Its pq ricx;8 l;j:zeriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o0l 1/ ib:fg8x4ivxc397gyhrx 4 ogpfxf 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 yeakc: rj s/ez y/ntc(.otnj)k 6ljs /6+urs. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [nj uj:jet okk+ .r6/)z c( cs/tln6/ysHint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about thkykw9*3 3jvui*o hlsj:g. fb *1sq a;ue center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, cv)dgwov+*.jn6tllw52: 3ss i0 et evperiod, and mean distance for the four largest moons of Jupiter (those discovered by Gal g:+2c5nw3) slive0 *dotts6jwve.l vileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known peri9*tfw qi0d-opr ;c 0otd: 2ayuc9p8in od and distance of the Moon. q0fou9pdp cnid:-9tca;ry8 0i* t w2o   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usin+i-td e huli-:es+7i lfr.- tpg Kepler’s third law. Use the distance of Io and the periods given in Table t.eei7t f- s+h- il+udp:- ril5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which sx *97ips8(jco 1nom coome space scientists think came from a planet that ooc pijs8* (7n om1oxc9nce orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an a9q9 9mulk0kps+df-p3l e-k4 dr4eobt rtificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. Whaep ubf dqk+k0-el-49sor 4lm9d9t3 kpt will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine+xh: jo6r 82zm1qj oi*eu j(eg (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.xe:jj eoo8jr 2i*q1u (g 6hm+z   

  How far above the Earth’s surface will the acceleration of gra58)d s hkq iasehlo4+h9 aj1t048bankvity be half what it is hlon9 a) e a8ja 4hsb1+4q8h si50dktkon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass g)nh 16jwj/xzdrab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 06 dnzwh)jx/ j1.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per d *scpugpu417i*cxe a1ay, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is thispe*g sui4* ac7cp 1xu1?    $\times 10^{-1}$

  At what distance from2 ji /zf1tpi( 6 0gfevi-iv:rm the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pul1ti v62r/ij(vfg:ifpm - 0ezil with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sc./ jrny a:n-kdale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator,nj/y.kd a-nr: and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about.b3r0x fhieuw/j+p/jdqj l 4( its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equx4+rq 0j h/jdeli(bp w3 ufj/.al to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig/t uk7d-3xm)tm1uq bu.at7mg . 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a mm0yg,5sr3)f+o 3nhble z nk4planet in terms of its radius r, the acceleration due telnf )k0yrh+5no3m34 g szmb,o gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a sq.b)j5dl- q (wuxnj5;nil 7r(-debty tring) is deflected from the vertical by an angle5 b7bq( dy(i;ln)wltux j .drjnq- 5-e $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If t02;6.vnwju4wil ji io9 g wi.phe coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a 4.wgwv0iiwipj6io.u29j;nl car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objec, u lgcp8jmardw sn+;z(c)mhv)6-8 r vts at the equator w)8(j)crwh lg86cvmnmdvs-+ p arz,; uere apparently weightless?    $\times 10^3$s

  Two equal-mass stars mait . ufn7qg(mhx)2s, 0ca3 kqd.jjd3nuntain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 24) j8sbpp q -xo3g2wrj35 m. A lamp suspended from the ceiling swings ou23 oqj-)bxg4 pr8s wpjt to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timesji. +: 0 tkjbg0w9 xk dmkjnid*c46cu) as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't surv0c)j .ui6kdm xd0 wkgtkb+4 ijn9jc:*ive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubbl 1/1(mbhcsg1 8dkt ijt2.k9p wqidyi 8e Space Telescope deduced the presence of an extremely1i1ptbcq2 ds9d 8jkhg8yi1iw/(.t k m massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a cob-0z )zfqv 5gmnstant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heqg -bvfz)0m5zaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of )js;ax( c6ue/er pz/g ul m(*i24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing contleug)are*cxm 6 (p(;/ /jzsiu inuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveli 0l4jq8lf q7rdng 2.1 billion km, is meant to orbit theql70d 4qfr lj8 asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuin xm(mq a5w-u2i0fet, qi/k2yrg a satellite in need of repair. You are in a circular orbit i,w0y(-qemt5 qkirx ma/fu22of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is itki i0+h67yacj j)n9yds mean distance from yaihid kj +70y96n )cjthe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G l i:lr96 y4 zj0gtlrd2 would need to be if you could actually "feel" yourself gravitationally attracted to someone neard : z2l ijrllyg6r904t you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around tmmf9 ix321wshhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 9m 21swi3h xfm30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 y p bovw )s3zr0hjein()p*+n0 m on each side. Find the magnitude and direction of the gravitational f ejyo0rhin zp0(nv*))+3w bp sorce on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 ko1-;w6gnb axr g orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by th (9 )9.hekvdnd7zuebce tip of the 1.5-cm-long sweep second hdk)9b. h7d u9en(vczeand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to zp* (mzs7d+1 (mvdqcwswing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makess d1v zzm(*(+ pwdmq7c with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desig-ieftxd67bp2i7 m 0o qned so that a car traveling at spitpd7x6eq0 i72o -mfb eed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars wh3s g(oxrz-mv9t1qm *.em ehve 8 r*9oaen negotiating curves. The angle of tez sm1m8*ox* 3vmreqeh - (ot9g9.r avilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$